Getting the Data and installing libraries

1. Introduction

The European Social Survey (ESS) is a large scale survey conducted in over 38 countries within Europe. Focusing on public attitudes and values and changes within time. This paper is evaluating the ninth version of the survey (ESS9) form 2018. The political landscape has been changed immensely after the start of the pandemic. Everyone has an opinion on everything remarkably political and does not shy away from posting it online. Furthermore, as a society we have upped the news consumption during the pandemic (see for Switzerland: https://medien.srf.ch/-/ein-von-corona-gepragtes-jahr-srf-mit-positiver-nutzungsbilanz). So the question that this analysis is looking to answer is: How was the political sentiment/actions during the last European Social Survey before Corona and how can interest, sentiment around politics and socio-demographic attributes contribute to the prediction of the political actions.

1.1 Selection of parameters

The survey is really comprehensive and consists out of 572 variables. Some of them are related to others and only answered by a subset of participants. Here is the link to the survey and their many variables: https://ess-search.nsd.no/en/study/bdc7c350-1029-4cb3-9d5e-53f668b8fa74

1.2 Goal

As already mentioned above the theme this paper is following is the of political “actions”. Moreover, the consumption of political news and online posting of current affairs is of important understanding considering the inhibition threshold is bigger than just talking to your family. If someone posts something online, then the person has to calculate the cost of the post for the future social interactions. The consumption of news is also connected to the thinking, a person could also consume another media content, that is much lighter and oftentimes more positive. Seemingly logical, interest in politic should have a positive relationship to these “actions”. However, also the thoughts how the state of the government, satisfaction and owns ability for politics have an influence on the “actions”. Next to these more politics covered predictors, there is also the socio-demographic aspect. E.g. with age, ones interest in politics rises. There also could be a gender gap and to not forget, education. The latter corresponds to political “actions” because with a higher education, one is more inclined to be able to follow current affairs because of the knowledge instilled in him during the higher education.

This paper will be following the following structure: Firstly the cleaning of the data, as there are a lot of variables there will be only cleaning of the variable that matter for this analysis. In a next step the models will be presented. The start will be made with the linear regression, then the two GLM models “Poisson” and “Binomial”. The third presented model is the GAM and the last two will be the “Neural Network” and Support Vector Machine. These models will be followed with a short conclusion.

2. Descriptive Statistics

## tibble [2,358 × 572] (S3: tbl_df/tbl/data.frame)
##  $ dweight : num [1:2358] 0.999 0.999 0.999 0.999 0.999 ...
##  $ pspwght : num [1:2358] 1.275 0.854 0.76 1.079 1.27 ...
##  $ pweight : num [1:2358] 3.04 3.04 3.04 3.04 3.04 ...
##  $ name    : chr [1:2358] "ESS9e03_1" "ESS9e03_1" "ESS9e03_1" "ESS9e03_1" ...
##  $ essround: num [1:2358] 9 9 9 9 9 9 9 9 9 9 ...
##  $ edition : num [1:2358] 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 ...
##  $ proddate: chr [1:2358] "17.02.2021" "17.02.2021" "17.02.2021" "17.02.2021" ...
##  $ idno    : num [1:2358] 9 10 64 65 91 119 150 212 255 270 ...
##  $ cntry   : chr [1:2358] "DE" "DE" "DE" "DE" ...
##  $ anweight: num [1:2358] 3.87 2.59 2.31 3.28 3.86 ...
##  $ prob    : num [1:2358] 0.000122 0.000122 0.000122 0.000122 0.000122 ...
##  $ stratum : num [1:2358] 336 284 307 338 297 323 320 295 294 278 ...
##  $ psu     : num [1:2358] 5856 5755 5798 5861 5779 ...
##  $ nwspol  : num [1:2358] 8 60 120 300 0 30 60 30 60 30 ...
##  $ netusoft: num [1:2358] 5 1 3 2 5 5 4 5 4 1 ...
##  $ netustm : num [1:2358] 480 6666 6666 6666 60 ...
##  $ ppltrst : num [1:2358] 5 7 7 7 5 3 3 6 7 8 ...
##  $ pplfair : num [1:2358] 5 8 7 6 6 6 4 5 7 9 ...
##  $ pplhlp  : num [1:2358] 5 5 5 3 6 5 4 5 8 9 ...
##  $ polintr : num [1:2358] 3 1 1 1 3 2 1 3 2 2 ...
##  $ psppsgva: num [1:2358] 4 4 2 3 2 3 3 3 2 3 ...
##  $ actrolga: num [1:2358] 3 4 2 2 3 1 3 1 3 2 ...
##  $ psppipla: num [1:2358] 3 4 3 2 3 8 3 2 2 3 ...
##  $ cptppola: num [1:2358] 3 4 3 3 4 4 3 2 4 3 ...
##  $ trstprl : num [1:2358] 2 7 3 3 4 9 10 5 5 7 ...
##  $ trstlgl : num [1:2358] 4 8 5 4 5 7 10 7 8 8 ...
##  $ trstplc : num [1:2358] 5 8 6 4 7 7 10 7 9 8 ...
##  $ trstplt : num [1:2358] 0 6 3 3 5 8 10 5 5 6 ...
##  $ trstprt : num [1:2358] 2 6 5 3 5 8 4 5 5 6 ...
##  $ trstep  : num [1:2358] 3 4 5 2 4 10 10 6 3 7 ...
##  $ trstun  : num [1:2358] 0 5 6 2 5 10 10 6 7 7 ...
##  $ vote    : num [1:2358] 2 1 1 1 1 1 1 1 1 1 ...
##  $ prtvtcat: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdbe: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdbg: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtgch: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtbcy: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtecz: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvede1: num [1:2358] 66 1 2 2 9 2 1 2 3 1 ...
##  $ prtvede2: num [1:2358] 66 1 2 2 88 1 1 2 3 1 ...
##  $ prtvtddk: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtgee: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtees: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdfi: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdfr: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcgb: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtahr: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtfhu: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcie: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcis: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcit: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvblt1: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvblt2: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvblt3: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtalv: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtme : num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtgnl: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtbno: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdpl: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcpt: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtrs : num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtcse: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtfsi: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtvtdsk: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ contplt : num [1:2358] 2 2 2 1 2 2 1 2 2 1 ...
##  $ wrkprty : num [1:2358] 2 2 2 2 2 2 2 2 2 1 ...
##  $ wrkorg  : num [1:2358] 1 2 1 1 1 2 1 2 2 2 ...
##  $ badge   : num [1:2358] 2 2 2 2 2 2 2 2 2 2 ...
##  $ sgnptit : num [1:2358] 2 2 2 2 1 2 1 2 1 2 ...
##  $ pbldmn  : num [1:2358] 2 1 2 2 2 2 2 2 1 2 ...
##  $ bctprd  : num [1:2358] 2 1 2 1 1 2 1 2 1 2 ...
##  $ pstplonl: num [1:2358] 2 2 2 2 1 2 2 2 2 2 ...
##  $ clsprty : num [1:2358] 2 1 1 1 2 2 1 1 1 1 ...
##  $ prtcldat: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtcldbe: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtcldbg: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclgch: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclbcy: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclecz: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclede: num [1:2358] 66 1 2 2 66 66 1 2 3 1 ...
##  $ prtclddk: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclgee: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclfes: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclefi: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclffr: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclcgb: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclahr: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclghu: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtcleie: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclcis: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtcldit: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclblt: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclalv: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclme : num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclfnl: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclbno: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclhpl: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclept: num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##  $ prtclrs : num [1:2358] NA NA NA NA NA NA NA NA NA NA ...
##   [list output truncated]

2.1 Cleaning of the data

3. Models

3.1 Linear Model

This chapter will be focused on the continous variable nwspol. The question in the survey was: On a typical day, about how much time do you spend watching, reading or listening to news about politics and current affairs?
The older the person, the more they watch the news. The same hypothesis can be made for education, satisfaction with democracy, confidence in own ability to participate and interest in politics.

Graphical analysis

This plot shows in the upper half news consumption variable with outliers. As can be seen, there are a lot of outliers. In the second half of the plot, there are no outliers and there can bee seen an increase in news consumption (interest in politics and confidence in ability) with every step.

Interpretation:
Age: The relationship between age and news consumption is not at every point positively linear. It starts to grow from the age smallest age (15y) to approximitely 25 and then it stagnates till around the age 50 and then the news consumption grows with every year. This can be explained that news consumption is not that important during the time between the ages 25 to 50 because of family matters such as raising children or focusing on career. Afterwards or beforehand the obligations are lighter.
Education in years: there is a small positive slope. This also confirms the hypothesis that with each additional educational year ones ability in understanding of current affairs is heightend and therefore one is more interested in news and consumes it more frequently. One of the reasons is the ability to understand it.

Fitting Model

## 
## Call:
## lm(formula = nwspol.na ~ age.na, data = ess9_linear)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
##  -92.23  -34.89  -15.36   13.66 1119.49 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 15.09729    4.62268   3.266              0.00111 ** 
## age.na       0.97636    0.08713  11.206 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 79.21 on 2294 degrees of freedom
## Multiple R-squared:  0.0519, Adjusted R-squared:  0.05149 
## F-statistic: 125.6 on 1 and 2294 DF,  p-value: < 0.00000000000000022

Interpretation: age is a highly significant predictor. It is a positive relationship to the news consumption in minute. The p-Value is <0.05. For every additional year a person nearly 1 minute (0.97) is added to the news consumption. This does not dismis the hypothesis that with every additional year, a person is following the news. There is the common knowledge that the older population is more likely to vote and that young people are more focused on other life topics.

Adding additional predictors

## 
## Call:
## lm(formula = nwspol.na ~ age.na + ability.fac, data = ess9_linear)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
##  -94.39  -34.31  -14.34   12.98 1118.68 
## 
## Coefficients:
##               Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)   16.78717    4.82835   3.477             0.000517 ***
## age.na         1.00102    0.08729  11.468 < 0.0000000000000002 ***
## ability.fac.L 23.91718    5.60431   4.268            0.0000206 ***
## ability.fac.Q  6.14664    4.96852   1.237             0.216170    
## ability.fac.C -0.16275    4.08717  -0.040             0.968240    
## ability.fac^4  1.05014    3.23978   0.324             0.745862    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 78.87 on 2290 degrees of freedom
## Multiple R-squared:  0.0616, Adjusted R-squared:  0.05956 
## F-statistic: 30.07 on 5 and 2290 DF,  p-value: < 0.00000000000000022

{drop1(lm_news.1, test = "F")}

Interpretation: the Variable Confidence in ability might have an influence on the dependent variable as it is significant in the single term deletions.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Fit: lm(formula = nwspol.na ~ age.na + ability.fac, data = ess9_linear)
## 
## Linear Hypotheses:
##                              Estimate Std. Error t value Pr(>|t|)    
## a little - not at all == 0      1.853      6.232   0.297  0.99818    
## quite - not at all == 0         9.132      6.186   1.476  0.56370    
## very - not at all == 0         17.185      6.786   2.533  0.07846 .  
## completely - not at all == 0   30.150      8.512   3.542  0.00346 ** 
## quite - a little == 0           7.279      4.029   1.806  0.35566    
## very - a little == 0           15.332      4.876   3.144  0.01348 *  
## completely - a little == 0     28.297      7.103   3.984  < 0.001 ***
## very - quite == 0               8.054      4.812   1.674  0.43565    
## completely - quite == 0        21.019      7.060   2.977  0.02268 *  
## completely - very == 0         12.965      7.576   1.711  0.41230    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)

Interpretation: When comparing the different self assumed levels of confidence in ones ability it is observable that the polar opposites completely and not at all have significant difference (p<.05) and the next biggest difference completely and a little are also significant. The others have a lower level of significants or none at all.

## 
## Call:
## lm(formula = nwspol.na ~ eduyrs.na + age.na + gndr.fac + stfdem.na + 
##     ability.fac + interest.fac, data = ess9_linear)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -100.69  -31.90  -12.93   13.30 1127.04 
## 
## Coefficients:
##                Estimate Std. Error t value           Pr(>|t|)    
## (Intercept)    49.64547   10.03733   4.946 0.0000008123487802 ***
## eduyrs.na      -0.96445    0.49499  -1.948            0.05149 .  
## age.na          0.71236    0.09329   7.636 0.0000000000000328 ***
## gndr.fac2      -2.69782    3.31452  -0.814            0.41576    
## stfdem.na      -1.03706    0.70387  -1.473            0.14079    
## ability.fac.L  10.55681    6.05077   1.745            0.08117 .  
## ability.fac.Q   7.68736    5.00224   1.537            0.12448    
## ability.fac.C   1.17460    4.04289   0.291            0.77143    
## ability.fac^4   0.98067    3.20308   0.306            0.75951    
## interest.fac.L 29.65914    6.75701   4.389 0.0000118846240809 ***
## interest.fac.Q 13.83210    5.04290   2.743            0.00614 ** 
## interest.fac.C -2.64438    3.33380  -0.793            0.42774    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 77.76 on 2284 degrees of freedom
## Multiple R-squared:  0.09036,    Adjusted R-squared:  0.08598 
## F-statistic: 20.62 on 11 and 2284 DF,  p-value: < 0.00000000000000022

Interpretation: Age and two expressions of the predictor variable interest in politics show signifcant values. Interest is here only significant in terms of the reference level. This linear regression also shows a higher adjusted R2 (0.085) then the one with the two predictors. However, it is still a small value and the model explains roughly 8% of the variations of the data.

##                     2.5 %       97.5 %
## (Intercept)    29.9622382 69.328698532
## eduyrs.na      -1.9351294  0.006238564
## age.na          0.5294131  0.895310385
## gndr.fac2      -9.1975974  3.801961940
## stfdem.na      -2.4173456  0.343229267
## ability.fac.L  -1.3087655 22.422383039
## ability.fac.Q  -2.1220445 17.496772989
## ability.fac.C  -6.7535159  9.102714457
## ability.fac^4  -5.3005776  7.261926573
## interest.fac.L 16.4086202 42.909662132
## interest.fac.Q  3.9429471 23.721250676
## interest.fac.C -9.1819647  3.893205185

Interaction: Age * ability

The background to this interaction: With every additional year on this earth one grows in his confidence in the own ability to participate in the political landscape. So therefore, the level of confidence in ones ability is dependent/varies on the age.

## 
## Call:
## lm(formula = nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac + 
##     stfdem.na + interest.fac, data = ess9_linear)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -117.14  -32.18  -13.15   13.67 1125.16 
## 
## Coefficients:
##                      Estimate Std. Error t value         Pr(>|t|)    
## (Intercept)           45.0916    10.5389   4.279 0.00001958665556 ***
## eduyrs.na             -0.9450     0.4967  -1.903           0.0572 .  
## age.na                 0.7880     0.1112   7.085 0.00000000000184 ***
## ability.fac.L        -18.9613    16.1182  -1.176           0.2396    
## ability.fac.Q         -9.8818    14.1288  -0.699           0.4844    
## ability.fac.C        -21.9343    11.4716  -1.912           0.0560 .  
## ability.fac^4        -13.6327     9.0569  -1.505           0.1324    
## gndr.fac2             -2.4310     3.3153  -0.733           0.4635    
## stfdem.na             -1.0179     0.7037  -1.447           0.1482    
## interest.fac.L        30.7487     6.7908   4.528 0.00000626223350 ***
## interest.fac.Q        13.1529     5.1038   2.577           0.0100 *  
## interest.fac.C        -2.4369     3.3424  -0.729           0.4660    
## age.na:ability.fac.L   0.5682     0.2901   1.959           0.0503 .  
## age.na:ability.fac.Q   0.3716     0.2571   1.445           0.1485    
## age.na:ability.fac.C   0.4680     0.2178   2.149           0.0317 *  
## age.na:ability.fac^4   0.3051     0.1740   1.753           0.0797 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 77.69 on 2280 degrees of freedom
## Multiple R-squared:  0.09361,    Adjusted R-squared:  0.08765 
## F-statistic:  15.7 on 15 and 2280 DF,  p-value: < 0.00000000000000022
## Single term deletions
## 
## Model:
## nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac + stfdem.na + 
##     interest.fac
##                    Df Sum of Sq      RSS   AIC
## <none>                          13759932 20003
## eduyrs.na           1     21851 13781784 20005
## gndr.fac            1      3245 13763177 20002
## stfdem.na           1     12628 13772560 20004
## interest.fac        3    408076 14168008 20064
## age.na:ability.fac  4     49448 13809380 20004

Interpretation: Nothing is significant, not even the interaction. The hypothesis on the interaction has to be dismissed. Also the adjusted R2 has not increased (a lot), therefore, this interaction is not useful.

##                               2.5 %      97.5 %
## (Intercept)           24.4246611513 65.75845544
## eduyrs.na             -1.9189916573  0.02889455
## age.na                 0.5698937223  1.00609375
## ability.fac.L        -50.5692499912 12.64663750
## ability.fac.Q        -37.5885428572 17.82493581
## ability.fac.C        -44.4301641545  0.56152951
## ability.fac^4        -31.3933160345  4.12783323
## gndr.fac2             -8.9322647665  4.07025536
## stfdem.na             -2.3979510424  0.36206988
## interest.fac.L        17.4318131927 44.06559034
## interest.fac.Q         3.1442173901 23.16150527
## interest.fac.C        -8.9914422606  4.11764654
## age.na:ability.fac.L  -0.0006799644  1.13710009
## age.na:ability.fac.Q  -0.1325726928  0.87579856
## age.na:ability.fac.C   0.0409404664  0.89515543
## age.na:ability.fac^4  -0.0361108509  0.64632065

The interaction is not significant. Therefore, let’s focus on the interest in politics variable

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Fit: lm(formula = nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac + 
##     stfdem.na + interest.fac, data = ess9_linear)
## 
## Linear Hypotheses:
##                           Estimate Std. Error t value Pr(>|t|)    
## hardly - none at all == 0   -1.581      9.232  -0.171 0.998059    
## quite - none at all == 0    15.439      9.390   1.644 0.333749    
## very - none at all == 0     40.164      9.852   4.077 0.000234 ***
## quite - hardly == 0         17.021      4.184   4.068 0.000233 ***
## very - hardly == 0          41.745      5.139   8.123 < 0.0001 ***
## very - quite == 0           24.724      4.353   5.679 < 0.0001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)

Interpretation: the different stages of political interest indicate a different usage of news according to the age. While the lowest level of political interest shows a positive relationship between news consumption and age, it has the the second smallest slope. The most interest category expression has the biggest slope over the lifetime.

Fitted Values and Residuals

Fitted Values

There are 185 unique fitted values from the first linear regression.

Residuals

Predicted values

one predictor variable

3.2 GLM Poisson

The goal of this chapter is to apply a generalized linear model of the poisson type on the ESS9 data set. The poisson model is applied to count data, in this case the information of how many minutes the participants spend per day for consuming media, such as newspaper, TV new shows or online resources.

In this chapter the model is used to simulate the data, based on the survey data. Getting a simulation of the minutes according to a selected subset of variables from the study.

First the data is cleaned and prepared for using it. A subset of the data is used, containing social and demographic variables which should help to model the news consumption of a person. These parameters are used:

Depended variable:

  • How much politics are you watching (“nwspol”)

Independent variables:

  1. Interest in politics (“polintr)
  2. Trust into the current parlament (“trstprl”)
  3. Highest level of education (“eisced”)
  4. Years of education (“eduyrs”)
  5. Satisfaction with the general economical situation (“stfeco”)
  6. Satisfaction with the current government (“stfgov”)
  7. Satisfaction with the democratic system (“stfdem”)
  8. Gender (“gndr”)
  9. Age (“agea”)
  10. Level of religiouse believes (“rlgdgr”)
  11. Time spent online in 5 categorical values(“netusoft”)
  12. Possibility for political participation (“psppsgva”)
  13. Yearly gross income (combination of two factors into a new one - “yrpy”)

3.2.1 Data preparation

The data have to be prepared and transformed. For poisson count data are needed for the predictive variable. The time in minutes is modeled therefore.

## [1] 572
## [1] 708
## [1] 1752
## [1] 47

Subset data for this task, to the defined 14 variables in total. The rows with NA are dropped, as the data set is large enough for dropping theses values.

## tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)
##  $ nwspol  : num [1:17029] 60 45 60 120 15 60 30 30 10 10 ...
##  $ polintr : Factor w/ 4 levels "1","2","3","4": 4 3 4 2 4 1 2 3 2 2 ...
##  $ trstprl : Factor w/ 11 levels "0","1","2","3",..: 7 1 1 7 5 4 4 8 8 6 ...
##  $ eisced  : Factor w/ 8 levels "1","2","3","4",..: 2 3 3 3 3 4 3 6 2 7 ...
##  $ eduyrs  : num [1:17029] 12 11 12 12 13 21 18 17 9 17 ...
##  $ stfeco  : Factor w/ 11 levels "0","1","2","3",..: 6 7 2 11 10 8 7 8 7 9 ...
##  $ stfgov  : Factor w/ 11 levels "0","1","2","3",..: 7 9 4 11 9 3 8 3 8 7 ...
##  $ stfdem  : Factor w/ 11 levels "0","1","2","3",..: 7 7 4 11 8 4 11 7 9 8 ...
##  $ gndr    : Factor w/ 2 levels "1","2": 2 1 1 1 2 1 1 1 1 1 ...
##  $ agea    : num [1:17029] 40 63 56 48 41 27 49 42 50 35 ...
##  $ rlgdgr  : Factor w/ 11 levels "0","1","2","3",..: 5 2 9 1 4 4 3 1 4 3 ...
##  $ netusoft: Factor w/ 5 levels "1","2","3","4",..: 4 5 1 1 4 5 5 5 5 5 ...
##  $ psppsgva: Factor w/ 5 levels "1","2","3","4",..: 2 2 2 5 1 3 1 1 2 3 ...
##  $ yrpy    : num [1:17029] 31200 30600 18000 31200 37200 18000 20400 17400 45600 70000 ...

The plot shows the media consumption for male and female to gain a quick overview. Males have a higher mean and the variance of values between the first and third quantile is larger as well in comparison.

The second plot indicates the frequency of internet usage and the media consumption. The mean of the two lower frequencies (“never” and “only occasionally”) have higher values for media consumption.

3.2.2 Fitting the poisson model

Using the parameter specified above to model the consumption. Using the subset variables of the survey.

## 
## Call:
## glm(formula = nwspol ~ polintr + eisced + trstprl + eduyrs + 
##     netusoft + stfeco + stfgov + stfdem + gndr + agea + rlgdgr + 
##     yrpy, family = "poisson", data = ess9_poisson)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -17.160   -6.476   -3.322    0.474   74.725  
## 
## Coefficients:
##                     Estimate       Std. Error  z value             Pr(>|z|)    
## (Intercept)  4.9551478455834  0.0105343674796  470.379 < 0.0000000000000002 ***
## polintr2    -0.3492665558265  0.0026678349780 -130.918 < 0.0000000000000002 ***
## polintr3    -0.5376726514740  0.0028816344085 -186.586 < 0.0000000000000002 ***
## polintr4    -0.6563093286586  0.0037354537637 -175.697 < 0.0000000000000002 ***
## eisced2     -0.1458105762706  0.0064736859414  -22.524 < 0.0000000000000002 ***
## eisced3     -0.2098897454780  0.0063900096516  -32.847 < 0.0000000000000002 ***
## eisced4     -0.0801180098272  0.0062959701053  -12.725 < 0.0000000000000002 ***
## eisced5     -0.1793751705951  0.0066035938535  -27.163 < 0.0000000000000002 ***
## eisced6     -0.0136582683597  0.0068047744981   -2.007               0.0447 *  
## eisced7     -0.0747622892396  0.0070310740541  -10.633 < 0.0000000000000002 ***
## eisced55     0.1991819464428  0.0184339911655   10.805 < 0.0000000000000002 ***
## trstprl1     0.0438116718767  0.0056421385757    7.765 0.000000000000008159 ***
## trstprl2     0.0878787242680  0.0050348881462   17.454 < 0.0000000000000002 ***
## trstprl3     0.0575992821977  0.0049226015149   11.701 < 0.0000000000000002 ***
## trstprl4     0.1649699717288  0.0049617090096   33.249 < 0.0000000000000002 ***
## trstprl5     0.1785393616823  0.0046962221481   38.018 < 0.0000000000000002 ***
## trstprl6     0.0926411783091  0.0050274726710   18.427 < 0.0000000000000002 ***
## trstprl7     0.1654323040088  0.0050166399191   32.977 < 0.0000000000000002 ***
## trstprl8     0.2017014330997  0.0053305193535   37.839 < 0.0000000000000002 ***
## trstprl9     0.1425488919881  0.0068020761893   20.957 < 0.0000000000000002 ***
## trstprl10    0.1034979576788  0.0080156227526   12.912 < 0.0000000000000002 ***
## eduyrs      -0.0047838263191  0.0003248431772  -14.727 < 0.0000000000000002 ***
## netusoft2   -0.1307787280215  0.0062823662011  -20.817 < 0.0000000000000002 ***
## netusoft3   -0.1124713541777  0.0061051654140  -18.422 < 0.0000000000000002 ***
## netusoft4   -0.1650624943097  0.0053911538839  -30.617 < 0.0000000000000002 ***
## netusoft5   -0.2565499520473  0.0047119730917  -54.446 < 0.0000000000000002 ***
## stfeco1      0.2042630443847  0.0078684572864   25.960 < 0.0000000000000002 ***
## stfeco2      0.1454844795976  0.0065882376682   22.082 < 0.0000000000000002 ***
## stfeco3      0.1097594146381  0.0063537352177   17.275 < 0.0000000000000002 ***
## stfeco4      0.1173993792901  0.0063956760982   18.356 < 0.0000000000000002 ***
## stfeco5      0.1060677186837  0.0062503682707   16.970 < 0.0000000000000002 ***
## stfeco6      0.0454950862456  0.0063907869403    7.119 0.000000000001088272 ***
## stfeco7     -0.0695855130540  0.0063960463742  -10.879 < 0.0000000000000002 ***
## stfeco8     -0.0844850487183  0.0065231751269  -12.952 < 0.0000000000000002 ***
## stfeco9     -0.1059951308680  0.0073197601880  -14.481 < 0.0000000000000002 ***
## stfeco10    -0.2077250234061  0.0087105452425  -23.848 < 0.0000000000000002 ***
## stfgov1     -0.0371282966740  0.0053909882570   -6.887 0.000000000005693961 ***
## stfgov2     -0.1628748230687  0.0050296948069  -32.383 < 0.0000000000000002 ***
## stfgov3     -0.1492579265587  0.0049582011543  -30.103 < 0.0000000000000002 ***
## stfgov4     -0.0842706452037  0.0050657063724  -16.636 < 0.0000000000000002 ***
## stfgov5     -0.0532296925917  0.0049390418045  -10.777 < 0.0000000000000002 ***
## stfgov6     -0.1646096319626  0.0052200210811  -31.534 < 0.0000000000000002 ***
## stfgov7     -0.0601493306535  0.0052887394475  -11.373 < 0.0000000000000002 ***
## stfgov8     -0.1257885537272  0.0059854927793  -21.016 < 0.0000000000000002 ***
## stfgov9      0.1018727906473  0.0080519498858   12.652 < 0.0000000000000002 ***
## stfgov10     0.0782407518655  0.0098315985238    7.958 0.000000000000001747 ***
## stfdem1     -0.0563098592349  0.0069113969117   -8.147 0.000000000000000372 ***
## stfdem2     -0.0025138003015  0.0061045169098   -0.412               0.6805    
## stfdem3     -0.1749548063588  0.0060699082915  -28.823 < 0.0000000000000002 ***
## stfdem4     -0.0834553121230  0.0061336706557  -13.606 < 0.0000000000000002 ***
## stfdem5     -0.0745510981878  0.0059070855389  -12.621 < 0.0000000000000002 ***
## stfdem6     -0.1142834927352  0.0061219691225  -18.668 < 0.0000000000000002 ***
## stfdem7     -0.0757921344766  0.0060426970153  -12.543 < 0.0000000000000002 ***
## stfdem8     -0.1281854636406  0.0062024480020  -20.667 < 0.0000000000000002 ***
## stfdem9     -0.1819244111818  0.0069479462167  -26.184 < 0.0000000000000002 ***
## stfdem10    -0.1081689324763  0.0079802880965  -13.555 < 0.0000000000000002 ***
## gndr2       -0.0955221839468  0.0018928147422  -50.466 < 0.0000000000000002 ***
## agea         0.0039442838404  0.0000752630756   52.407 < 0.0000000000000002 ***
## rlgdgr1      0.0524594264550  0.0039129662333   13.407 < 0.0000000000000002 ***
## rlgdgr2      0.0229590182679  0.0037164081451    6.178 0.000000000650240197 ***
## rlgdgr3      0.1252369296839  0.0035904157083   34.881 < 0.0000000000000002 ***
## rlgdgr4      0.0911051329206  0.0040471525705   22.511 < 0.0000000000000002 ***
## rlgdgr5      0.0008947887099  0.0032698289371    0.274               0.7844    
## rlgdgr6      0.0599344542248  0.0035893248803   16.698 < 0.0000000000000002 ***
## rlgdgr7     -0.0077316837152  0.0035782505209   -2.161               0.0307 *  
## rlgdgr8      0.0079295142834  0.0038527509859    2.058               0.0396 *  
## rlgdgr9     -0.0750978361239  0.0059677036213  -12.584 < 0.0000000000000002 ***
## rlgdgr10     0.1758154007801  0.0047371153192   37.114 < 0.0000000000000002 ***
## yrpy        -0.0000000085380  0.0000000005367  -15.907 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 1622523  on 17028  degrees of freedom
## Residual deviance: 1532064  on 16960  degrees of freedom
## AIC: 1622455
## 
## Number of Fisher Scoring iterations: 6

The summary shows the residual deviance as 1532064 on 16960 degrees of freedom. This indicates an overdispersion as the difference between these two numbers is large. For an non-overdispersed result the should be similar or the same.

To compare the model for the two gender, the coefficient can be calculated.

##        (Intercept)           polintr2           polintr3           polintr4 
##  4.955147845583398 -0.349266555826538 -0.537672651474009 -0.656309328658579 
##            eisced2            eisced3            eisced4            eisced5 
## -0.145810576270611 -0.209889745477968 -0.080118009827152 -0.179375170595105 
##            eisced6            eisced7           eisced55           trstprl1 
## -0.013658268359742 -0.074762289239633  0.199181946442816  0.043811671876679 
##           trstprl2           trstprl3           trstprl4           trstprl5 
##  0.087878724267998  0.057599282197725  0.164969971728847  0.178539361682290 
##           trstprl6           trstprl7           trstprl8           trstprl9 
##  0.092641178309068  0.165432304008800  0.201701433099665  0.142548891988131 
##          trstprl10             eduyrs          netusoft2          netusoft3 
##  0.103497957678787 -0.004783826319139 -0.130778728021462 -0.112471354177693 
##          netusoft4          netusoft5            stfeco1            stfeco2 
## -0.165062494309659 -0.256549952047336  0.204263044384658  0.145484479597629 
##            stfeco3            stfeco4            stfeco5            stfeco6 
##  0.109759414638132  0.117399379290054  0.106067718683748  0.045495086245550 
##            stfeco7            stfeco8            stfeco9           stfeco10 
## -0.069585513054008 -0.084485048718322 -0.105995130868024 -0.207725023406075 
##            stfgov1            stfgov2            stfgov3            stfgov4 
## -0.037128296673999 -0.162874823068651 -0.149257926558705 -0.084270645203717 
##            stfgov5            stfgov6            stfgov7            stfgov8 
## -0.053229692591687 -0.164609631962625 -0.060149330653520 -0.125788553727176 
##            stfgov9           stfgov10            stfdem1            stfdem2 
##  0.101872790647289  0.078240751865529 -0.056309859234943 -0.002513800301504 
##            stfdem3            stfdem4            stfdem5            stfdem6 
## -0.174954806358804 -0.083455312122970 -0.074551098187797 -0.114283492735243 
##            stfdem7            stfdem8            stfdem9           stfdem10 
## -0.075792134476610 -0.128185463640629 -0.181924411181762 -0.108168932476321 
##              gndr2               agea            rlgdgr1            rlgdgr2 
## -0.095522183946788  0.003944283840447  0.052459426455015  0.022959018267916 
##            rlgdgr3            rlgdgr4            rlgdgr5            rlgdgr6 
##  0.125236929683865  0.091105132920631  0.000894788709914  0.059934454224848 
##            rlgdgr7            rlgdgr8            rlgdgr9           rlgdgr10 
## -0.007731683715226  0.007929514283363 -0.075097836123885  0.175815400780054 
##               yrpy 
## -0.000000008538016
##  gndr2 
## 0.9089

Female do consume approx. 10% less media compared to male participants.

3.2.3 Simulation

Now we simulate with our model the average media consumption for Females and Males.

## [1] 17029
##   sim_1
## 1    48
## 2    47
## 3    53
## 4    81
## 5    44
## 6    79

The simulated data look similar as the real data based of the survey. The variance is smaller for the simulated one. The higher mean and the higher variance for the male group is indicated in the real data as well as in the simulated data.

3.2.4 GLM Quasi-Poisson

In chapter 3.2.2 the data showed a overdispersion for the poisson model. This isn’t unusual and can be handled by the quasipoisson model type. The value for the dispersion parameter of 206.3327 indicates a much faster increase of variance than linearly.

## 
## Call:
## glm(formula = nwspol ~ polintr + eisced + trstprl + eduyrs + 
##     netusoft + stfeco + stfgov + stfdem + gndr + agea + rlgdgr + 
##     yrpy, family = "quasipoisson", data = ess9_poisson)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -17.160   -6.476   -3.322    0.474   74.725  
## 
## Coefficients:
##                    Estimate      Std. Error t value             Pr(>|t|)    
## (Intercept)  4.955147845583  0.151318671203  32.746 < 0.0000000000000002 ***
## polintr2    -0.349266555827  0.038321545611  -9.114 < 0.0000000000000002 ***
## polintr3    -0.537672651474  0.041392621858 -12.990 < 0.0000000000000002 ***
## polintr4    -0.656309328659  0.053657127583 -12.232 < 0.0000000000000002 ***
## eisced2     -0.145810576271  0.092989878732  -1.568             0.116894    
## eisced3     -0.209889745478  0.091787928543  -2.287             0.022227 *  
## eisced4     -0.080118009827  0.090437117569  -0.886             0.375685    
## eisced5     -0.179375170595  0.094855913182  -1.891             0.058638 .  
## eisced6     -0.013658268360  0.097745729573  -0.140             0.888873    
## eisced7     -0.074762289240  0.100996361201  -0.740             0.459160    
## eisced55     0.199181946443  0.264791128042   0.752             0.451927    
## trstprl1     0.043811671877  0.081045294240   0.541             0.588802    
## trstprl2     0.087878724268  0.072322575173   1.215             0.224347    
## trstprl3     0.057599282198  0.070709657845   0.815             0.415319    
## trstprl4     0.164969971729  0.071271409098   2.315             0.020643 *  
## trstprl5     0.178539361682  0.067457879792   2.647             0.008136 ** 
## trstprl6     0.092641178309  0.072216057163   1.283             0.199568    
## trstprl7     0.165432304009  0.072060452413   2.296             0.021703 *  
## trstprl8     0.201701433100  0.076569106494   2.634             0.008440 ** 
## trstprl9     0.142548891988  0.097706970293   1.459             0.144599    
## trstprl10    0.103497957679  0.115138700652   0.899             0.368720    
## eduyrs      -0.004783826319  0.004666140422  -1.025             0.305273    
## netusoft2   -0.130778728021  0.090241707193  -1.449             0.147299    
## netusoft3   -0.112471354178  0.087696344343  -1.283             0.199682    
## netusoft4   -0.165062494310  0.077440078253  -2.131             0.033063 *  
## netusoft5   -0.256549952047  0.067684130856  -3.790             0.000151 ***
## stfeco1      0.204263044385  0.113024773751   1.807             0.070742 .  
## stfeco2      0.145484479598  0.094635332540   1.537             0.124234    
## stfeco3      0.109759414638  0.091266872185   1.203             0.229140    
## stfeco4      0.117399379290  0.091869323004   1.278             0.201304    
## stfeco5      0.106067718684  0.089782079758   1.181             0.237464    
## stfeco6      0.045495086246  0.091799093740   0.496             0.620187    
## stfeco7     -0.069585513054  0.091874641754  -0.757             0.448823    
## stfeco8     -0.084485048718  0.093700755564  -0.902             0.367257    
## stfeco9     -0.105995130868  0.105143131500  -1.008             0.313419    
## stfeco10    -0.207725023406  0.125120766301  -1.660             0.096893 .  
## stfgov1     -0.037128296674  0.077437699141  -0.479             0.631617    
## stfgov2     -0.162874823069  0.072247976560  -2.254             0.024185 *  
## stfgov3     -0.149257926559  0.071221021260  -2.096             0.036124 *  
## stfgov4     -0.084270645204  0.072765256999  -1.158             0.246833    
## stfgov5     -0.053229692592  0.070945810873  -0.750             0.453093    
## stfgov6     -0.164609631963  0.074981877665  -2.195             0.028154 *  
## stfgov7     -0.060149330654  0.075968967960  -0.792             0.428511    
## stfgov8     -0.125788553727  0.085977332347  -1.463             0.143474    
## stfgov9      0.101872790647  0.115660513996   0.881             0.378443    
## stfgov10     0.078240751866  0.141223896670   0.554             0.579573    
## stfdem1     -0.056309859235  0.099277284456  -0.567             0.570587    
## stfdem2     -0.002513800302  0.087687029042  -0.029             0.977130    
## stfdem3     -0.174954806359  0.087189900939  -2.007             0.044809 *  
## stfdem4     -0.083455312123  0.088105801797  -0.947             0.343542    
## stfdem5     -0.074551098188  0.084851068293  -0.879             0.379625    
## stfdem6     -0.114283492735  0.087937717623  -1.300             0.193757    
## stfdem7     -0.075792134477  0.086799030374  -0.873             0.382571    
## stfdem8     -0.128185463641  0.089093739295  -1.439             0.150234    
## stfdem9     -0.181924411182  0.099802289140  -1.823             0.068344 .  
## stfdem10    -0.108168932476  0.114631143533  -0.944             0.345374    
## gndr2       -0.095522183947  0.027188933002  -3.513             0.000444 ***
## agea         0.003944283840  0.001081100371   3.648             0.000265 ***
## rlgdgr1      0.052459426455  0.056206967531   0.933             0.350665    
## rlgdgr2      0.022959018268  0.053383550864   0.430             0.667145    
## rlgdgr3      0.125236929684  0.051573759421   2.428             0.015180 *  
## rlgdgr4      0.091105132921  0.058134458505   1.567             0.117099    
## rlgdgr5      0.000894788710  0.046968759233   0.019             0.984801    
## rlgdgr6      0.059934454225  0.051558090456   1.162             0.245063    
## rlgdgr7     -0.007731683715  0.051399015186  -0.150             0.880431    
## rlgdgr8      0.007929514283  0.055342018474   0.143             0.886069    
## rlgdgr9     -0.075097836124  0.085721803787  -0.876             0.381007    
## rlgdgr10     0.175815400780  0.068045281012   2.584             0.009780 ** 
## yrpy        -0.000000008538  0.000000007710  -1.107             0.268132    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 206.3327)
## 
##     Null deviance: 1622523  on 17028  degrees of freedom
## Residual deviance: 1532064  on 16960  degrees of freedom
## AIC: NA
## 
## Number of Fisher Scoring iterations: 6
## Analysis of Deviance Table
## 
## Model 1: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco + 
##     stfgov + stfdem + gndr + agea + rlgdgr + yrpy
## Model 2: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco + 
##     stfgov + stfdem + agea + rlgdgr + yrpy
##   Resid. Df Resid. Dev Df Deviance     F    Pr(>F)    
## 1     16960    1532064                                
## 2     16961    1534617 -1  -2552.4 12.37 0.0004373 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Yes, Gender plays a role for the quasi poisson model. This can be assured with this test.

## Analysis of Deviance Table
## 
## Model 1: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco + 
##     stfgov + stfdem + gndr + agea + rlgdgr + yrpy
## Model 2: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco + 
##     stfgov + gndr + agea + rlgdgr + yrpy
##   Resid. Df Resid. Dev  Df Deviance      F Pr(>F)
## 1     16960    1532064                           
## 2     16970    1534358 -10  -2293.3 1.1114 0.3488

To compare it with the variable of “stfdem” about how satisfied the participants of the survey are about how the democracy in their country works. This variable doesn’t play a role to predict the media consumption according to the quasipoisson model.

The results can be concluded that according to the models there is some evidence, that the factors Interest in politics, age, and gender are influencing the media consumption.

3.3 GLM Binomial

For the binary data we are using the following question from the survey: There are different ways of trying to improve things in [country] or help prevent things from going wrong. During the last 12 months, have you done any of the following? Have you... ...posted or shared anything about politics online, for example on blogs, via email or on social media such as Facebook or Twitter?

Graphical Analysis

Fitting the binary model (logistic regression)

If someone posts online is dependent on the age of the person. Older people are not that tech-savy and therefore, have a higher inhibition to post online. On the other hand, young people grew up with social media and therefore are more likely to post political induced things.

## 
## Call:
## glm(formula = postonline ~ age.na, family = "binomial", data = ess9_binary.na)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.9792  -0.7141  -0.5696  -0.4445   2.1626  
## 
## Coefficients:
##              Estimate Std. Error z value            Pr(>|z|)    
## (Intercept) -0.069127   0.140640  -0.492               0.623    
## age.na      -0.027793   0.002954  -9.408 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2232.0  on 2211  degrees of freedom
## Residual deviance: 2138.1  on 2210  degrees of freedom
## AIC: 2142.1
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = postonline ~ age.na + eduyrs.na + interest.fac + 
##     boycott.fac + vote.fac, family = "binomial", data = ess9_binary.na)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.4233  -0.7072  -0.5132  -0.2928   2.5577  
## 
## Coefficients:
##                       Estimate Std. Error z value             Pr(>|z|)    
## (Intercept)           0.095283   0.363131   0.262             0.793018    
## age.na               -0.038720   0.003683 -10.513 < 0.0000000000000002 ***
## eduyrs.na             0.034592   0.017497   1.977             0.048043 *  
## interest.fac.L        1.135895   0.293125   3.875             0.000107 ***
## interest.fac.Q        0.195537   0.222651   0.878             0.379824    
## interest.fac.C        0.016625   0.133436   0.125             0.900846    
## boycott.fac2         -0.674136   0.116343  -5.794        0.00000000686 ***
## vote.facNo           -0.064151   0.206937  -0.310             0.756560    
## vote.facNot eligible -0.018313   0.201498  -0.091             0.927585    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 2232.0  on 2211  degrees of freedom
## Residual deviance: 2006.8  on 2203  degrees of freedom
## AIC: 2024.8
## 
## Number of Fisher Scoring iterations: 5
##          (Intercept)               age.na            eduyrs.na 
##            1.0999705            0.9620199            1.0351970 
##       interest.fac.L       interest.fac.Q       interest.fac.C 
##            3.1139580            1.2159638            1.0167642 
##         boycott.fac2           vote.facNo vote.facNot eligible 
##            0.5095967            0.9378635            0.9818538

Interpretation: By increasing the age by one year, the risk in odds will be increasing by approx. 1 time to post something political online.
The odds for posting online by having a low interest in politics is about 3.1 times higher than for persons that have no interest at all.

Estimating the performance of a binary model

simple binary model

##    fit
## obs    0    1
##   0  255 1508
##   1  108  341
##    fit
## obs    0    1
##   0 0.12 0.68
##   1 0.05 0.15

Interpretation: The table for the simple binary model (only one predictor) reveals that only 27 % of the observed data points have been correctly categorized (0 = did not post online; 1 = posted online). One reason for this low correct labeling could be the 0.3 used as a “cutoff” tool. However, by using the usually utilized 0.5 as a “cutoff” number there would not have been any observation for the level posted online. This is a trade-off the authors of this paper are aware of and it is a limitation of this analysis. The reason behind this predictor variable is the less “tech-saviness” of the older generation and therefore a less probability of them posting online about political matters.

more complex binary model

##    fitted
## obs    0    1
##   0   22 1741
##   1   19  430
##    fit
## obs    0    1
##   0   22 1741
##   1   19  430
##    fit
## obs    0    1
##   0 0.01 0.79
##   1 0.01 0.19

Interpretation: Meanwhile with the more complex binary model (more than one predictor) and the usage of the right number for the “cutoff” and the properly estimated data points are at 20%. This is also an under performing model.

3.4 GAM

In this chapter a generalized additive model (GAM) is applied to the data set. First the data is visually analyzed and checked. The variables don’t show a strong relation ship and the line is mostly horizontal.

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## (as.numeric(netusoft)) ~ yrpy + s(nwspol) + s(agea) + s(eduyrs, 
##     k = 1)
## 
## Parametric coefficients:
##                   Estimate     Std. Error t value             Pr(>|t|)    
## (Intercept) 4.576080568621 0.007178174263 637.499 < 0.0000000000000002 ***
## yrpy        0.000000019022 0.000000003969   4.792           0.00000166 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##             edf Ref.df     F              p-value    
## s(nwspol) 4.179  5.020   4.8             0.000208 ***
## s(agea)   7.661  7.956 207.2 < 0.0000000000000002 ***
## s(eduyrs) 1.996  2.000 512.0 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Rank: 20/22
## R-sq.(adj) =  0.156   Deviance explained = 15.6%
## GCV = 0.81683  Scale est. = 0.81607   n = 17029

The number of education years has a “edf” value of 1.9 this means it isn’t linear but has the lowest value of the three parameter and the model can be refitted and removing the smoothing factor.

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## (as.numeric(netusoft)) ~ yrpy + s(nwspol) + s(agea) + eduyrs
## 
## Parametric coefficients:
##                   Estimate     Std. Error t value             Pr(>|t|)    
## (Intercept) 3.790355942179 0.026881750691 141.001 < 0.0000000000000002 ***
## yrpy        0.000000019886 0.000000003981   4.995          0.000000594 ***
## eduyrs      0.054901261993 0.001824098908  30.098 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##             edf Ref.df       F              p-value    
## s(nwspol) 4.179  5.019   5.034             0.000124 ***
## s(agea)   7.128  7.746 223.705 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Rank: 19/21
## R-sq.(adj) =   0.15   Deviance explained = 15.1%
## GCV = 0.8222  Scale est. = 0.82151   n = 17029

The parameter age and news consumption can be compared for the two GAM models. It is visible that both are non-linear and only age changes in comparison of the two models.

3.5 Neural Network

Additional to “classic” linear models and GLM options, there are neural networks for analyzing and predicting data.

Within this chapter two types of neural network model are applied to two different questions.

  1. Predicting the values for the continuous variable
  2. Predicting the values for the categorical variable indicating the 5 levels of frequency of usage of internet

3.5.1 continious variable

## tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)
##  $ nwspol  : num [1:17029] 60 45 60 120 15 60 30 30 10 10 ...
##  $ polintr : num [1:17029] 4 3 4 2 4 1 2 3 2 2 ...
##  $ trstprl : num [1:17029] 6 0 0 6 4 3 3 7 7 5 ...
##  $ eisced  : num [1:17029] 2 3 3 3 3 4 3 6 2 7 ...
##  $ eduyrs  : num [1:17029] 12 11 12 12 13 21 18 17 9 17 ...
##  $ stfeco  : num [1:17029] 5 6 1 10 9 7 6 7 6 8 ...
##  $ stfgov  : num [1:17029] 6 8 3 10 8 2 7 2 7 6 ...
##  $ stfdem  : num [1:17029] 6 6 3 10 7 3 10 6 8 7 ...
##  $ gndr    : num [1:17029] 2 1 1 1 2 1 1 1 1 1 ...
##  $ agea    : num [1:17029] 40 63 56 48 41 27 49 42 50 35 ...
##  $ rlgdgr  : num [1:17029] 4 1 8 0 3 3 2 0 3 2 ...
##  $ netusoft: num [1:17029] 4 5 1 1 4 5 5 5 5 5 ...
##  $ psppsgva: num [1:17029] 2 2 2 5 1 3 1 1 2 3 ...
##  $ yrpy    : num [1:17029] 31200 30600 18000 31200 37200 18000 20400 17400 45600 70000 ...

Prepare for Training

Fit the Network

Predict the test set

And calculate the RMSE

## [1] 131.4847

Redo with caret and Cross Validation

```{#{r caret applied again, collapse=TRUE, message=FALSE, warning=FALSE} #set.seed(42) #tuGrid <- expand.grid(.layer1=c(1:2), .layer2=c(0,2), .layer3=c(0))

#trCtrl <- trainControl( # method = ‘repeatedcv’, #number = 4, # repeats = 8, # returnResamp = ‘final’ #)

#models <- train( # x = ess9_ann %>% dplyr::select(-nwspol), # y = ess9_ann_scaled %>% pull(nwspol), # method = ‘neuralnet’, metric = ‘RMSE’, # linear.output = FALSE, # be careful, does only work on x! #preProcess = c(‘center’, ‘scale’), #tuneGrid = tuGrid, #trControl = trCtrl #)


<img src="ESS_DE_files/figure-html/unnamed-chunk-41-1.png" width="672" />



and extract the best model



### 3.5.2 Categorical variable

NN models can be used for categorical variables as well. In this chapter the goal is to find a classification of values to the categories. As variable the frequency of usage of the internet is used.

tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)

$ nwspol : num [1:17029] 60 45 60 120 15 60 30 30 10 10 …

$ polintr : num [1:17029] 4 3 4 2 4 1 2 3 2 2 …

$ trstprl : num [1:17029] 6 0 0 6 4 3 3 7 7 5 …

$ eisced : num [1:17029] 2 3 3 3 3 4 3 6 2 7 …

$ eduyrs : num [1:17029] 12 11 12 12 13 21 18 17 9 17 …

$ stfeco : num [1:17029] 5 6 1 10 9 7 6 7 6 8 …

$ stfgov : num [1:17029] 6 8 3 10 8 2 7 2 7 6 …

$ stfdem : num [1:17029] 6 6 3 10 7 3 10 6 8 7 …

$ gndr : num [1:17029] 2 1 1 1 2 1 1 1 1 1 …

$ agea : num [1:17029] 40 63 56 48 41 27 49 42 50 35 …

$ rlgdgr : num [1:17029] 4 1 8 0 3 3 2 0 3 2 …

$ netusoft: Factor w/ 5 levels “1”,“2”,“3”,“4”,..: 4 5 1 1 4 5 5 5 5 5 …

$ psppsgva: num [1:17029] 2 2 2 5 1 3 1 1 2 3 …

$ yrpy : num [1:17029] 31200 30600 18000 31200 37200 18000 20400 17400 45600 70000 …


#### Have a quick look at the Data

<img src="ESS_DE_files/figure-html/unnamed-chunk-45-1.png" width="672" />

<img src="ESS_DE_files/figure-html/unnamed-chunk-46-1.png" width="672" />

#### Prepare the Data for Training



The distribution of our different prediction classes in the train and test data sets can be compared. The data shows a concentration of 4 and 5 values. The participants of this survey are often and frequently using the internet.

train

netusoft FALSE TRUE

1 90 515

2 91 516

3 106 604

4 210 1193

5 2055 11649




#### Train the Neural Network

Call the `neuralnet` function creating a network with two hidden layer.



Plot the resulting network including the weights



#### Make Predictions

[,1] [,2] [,3] [,4] [,5]

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[1754,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1755,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1756,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525

[1757,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1758,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1759,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1760,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1761,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1762,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1763,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1764,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1765,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1766,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1767,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1768,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1769,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1770,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1771,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1772,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1773,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525

[1774,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1775,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1776,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1777,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1778,] 0.033739567 0.03489626 0.04111957 0.08108409 0.80916056

[1779,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1780,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1781,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1782,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1783,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1784,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1785,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1786,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1787,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1788,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1789,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1790,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1791,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1792,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1793,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1794,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1795,] 0.019347109 0.02903874 0.03639421 0.07070488 0.84451365

[1796,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1797,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1798,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1799,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1800,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1801,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1802,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1803,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1804,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1805,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1806,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1807,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1808,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1809,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1810,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1811,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1812,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1813,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1814,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1815,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1816,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1817,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1818,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1819,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1820,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1821,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1822,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1823,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1824,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1825,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1826,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1827,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1828,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1829,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1830,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1831,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1832,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1833,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1834,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1835,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1836,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1837,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1838,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1839,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1840,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1841,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1842,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1843,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1844,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1845,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1846,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1847,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1848,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1849,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1850,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1851,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1852,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1853,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1854,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1855,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1856,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1857,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1858,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1859,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1860,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1861,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1862,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1863,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1864,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1865,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1866,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1867,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1868,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1869,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1870,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1871,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1872,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1873,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1874,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1875,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1876,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1877,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1878,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1879,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1880,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1881,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1882,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1883,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1884,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1885,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1886,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1887,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1888,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1889,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1890,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1891,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1892,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1893,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1894,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1895,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1896,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1897,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1898,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1899,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1900,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1901,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1902,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1903,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1904,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1905,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1906,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1907,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1908,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1909,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1910,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1911,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1912,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1913,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1914,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1915,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1916,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1917,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1918,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1919,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1920,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1921,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1922,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1923,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1924,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1925,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1926,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1927,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1928,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1929,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1930,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1931,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1932,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1933,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1934,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1935,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525

[1936,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1937,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1938,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1939,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1940,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1941,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1942,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1943,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1944,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1945,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[1946,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1947,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1948,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1949,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1950,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1951,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1952,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1953,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1954,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1955,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1956,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1957,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1958,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1959,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1960,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1961,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1962,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1963,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1964,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1965,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1966,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1967,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1968,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1969,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1970,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1971,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1972,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1973,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1974,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1975,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1976,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1977,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1978,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1979,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1980,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1981,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1982,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1983,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1984,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1985,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1986,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1987,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1988,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1989,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1990,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1991,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1992,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1993,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1994,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1995,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1996,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1997,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1998,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[1999,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2000,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2001,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2002,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2003,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2004,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2005,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2006,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2007,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2008,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2009,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2010,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2011,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2012,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2013,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2014,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2015,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2016,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2017,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2018,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2019,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2020,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2021,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2022,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2023,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2024,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2025,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2026,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2027,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2028,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2029,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2030,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2031,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2032,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2033,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2034,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2035,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2036,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2037,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2038,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2039,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2040,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2041,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2042,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2043,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2044,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2045,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2046,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2047,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2048,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2049,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2050,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2051,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2052,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2053,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2054,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2055,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2056,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2057,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2058,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2059,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2060,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2061,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2062,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2063,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2064,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2065,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2066,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2067,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2068,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2069,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2070,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2071,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2072,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2073,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2074,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2075,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2076,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2077,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2078,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2079,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2080,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2081,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2082,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2083,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2084,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2085,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2086,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2087,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2088,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2089,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2090,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2091,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2092,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2093,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2094,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2095,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2096,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2097,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2098,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2099,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2100,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2101,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2102,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2103,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2104,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2105,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2106,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2107,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2108,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2109,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2110,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2111,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2112,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2113,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2114,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2115,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2116,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2117,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2118,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2119,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2120,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2121,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2122,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2123,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2124,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2125,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2126,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2127,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2128,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2129,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2130,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2131,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2132,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2133,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2134,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2135,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2136,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2137,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2138,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2139,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2140,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2141,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2142,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2143,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2144,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2145,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2146,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2147,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2148,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2149,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2150,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2151,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2152,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2153,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2154,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2155,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2156,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2157,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2158,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2159,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2160,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2161,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2162,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2163,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2164,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2165,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2166,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2167,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2168,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2169,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2170,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2171,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2172,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2173,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2174,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2175,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2176,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2177,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2178,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2179,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2180,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2181,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

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[2186,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

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[2451,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2452,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2453,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2454,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2455,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2456,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2457,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2458,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2459,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2460,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2461,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2462,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2463,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2464,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2465,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2466,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2467,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2468,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2469,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2470,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2471,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2472,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2473,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2474,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2475,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2476,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2477,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2478,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2479,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2480,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2481,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2482,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2483,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2484,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2485,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2486,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2487,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2488,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2489,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2490,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2491,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2492,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2493,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2494,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2495,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2496,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2497,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2498,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2499,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2500,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2501,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2502,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2503,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854

[2504,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2505,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2506,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2507,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2508,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2509,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2510,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2511,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2512,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2513,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2514,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2515,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2516,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2517,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2518,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2519,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2520,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525

[2521,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2522,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2523,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2524,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2525,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2526,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2527,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525

[2528,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2529,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2530,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2531,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2532,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2533,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2534,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2535,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2536,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2537,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2538,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2539,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2540,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2541,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2542,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2543,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2544,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2545,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2546,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2547,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2548,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2549,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2550,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2551,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646

[2552,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646


Find class (i.e. output neuron) with the highest probability and convert this back into a factor

[1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[38] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[75] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[112] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[149] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[186] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[223] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[260] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[297] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[334] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[371] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[408] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[445] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[482] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[519] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[556] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[593] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[630] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[667] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[704] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[741] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[778] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[815] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[852] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[889] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[926] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[963] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1000] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1037] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1074] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1111] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1148] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1185] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1222] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1259] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1296] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1333] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1370] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1407] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1444] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1481] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1518] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1555] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1592] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1629] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1666] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1703] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1740] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1777] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1814] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1851] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1888] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1925] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1962] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[1999] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2036] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2073] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2110] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2147] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2184] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2221] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2258] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2295] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5

[2332] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2369] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2406] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2443] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2480] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

[2517] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Levels: 1 2 3 4 5


#### Evaluate the Results

The confusion maztrix shows

Confusion Matrix and Statistics

Reference

Prediction 1 2 3 4 5

1 1 0 0 0 89

2 0 0 0 0 91

3 0 0 0 0 106

4 0 0 0 0 210

5 0 0 0 0 2055

Overall Statistics

Accuracy : 0.8056

95% CI : (0.7897, 0.8208)

No Information Rate : 0.9996

P-Value [Acc > NIR] : 1

Kappa : 0.0036

Mcnemar’s Test P-Value : NA

Statistics by Class:

Class: 1 Class: 2 Class: 3 Class: 4 Class: 5

Sensitivity 1.0000000 NA NA NA 0.805566

Specificity 0.9651117 0.96434 0.95846 0.91771 1.000000

Pos Pred Value 0.0111111 NA NA NA 1.000000

Neg Pred Value 1.0000000 NA NA NA 0.002012

Prevalence 0.0003918 0.00000 0.00000 0.00000 0.999608

Detection Rate 0.0003918 0.00000 0.00000 0.00000 0.805251

Detection Prevalence 0.0352665 0.03566 0.04154 0.08229 0.805251

Balanced Accuracy 0.9825559 NA NA NA 0.902783


#### Optimize Network Structure

First we need to remodel the data due to some limitations of `caret`

netusoft netusoft2 netusoft3 netusoft4 netusoft5

1 1 0 0 1 0

2 1 0 0 0 1

3 1 0 0 0 0

4 1 0 0 0 0

5 1 0 0 1 0

6 1 0 0 0 1






And have a look at the different models

<img src="ESS_DE_files/figure-html/unnamed-chunk-55-1.png" width="672" />

And try out the best model



The error for both types of neutral network model is still high, the optimization options were limited, as changing variables lead to high computing times. Nevertheless the models predict values for the two chosen variables. The continuous model lead to better results, comparing the calculated errors.

## 3.6 Support Vector Machine

The goal in this chapter is to classify people on their political scale. Leftist on the left, center on the center and right-wing people on the right. The response variable *scale_cat* is in the survey categorized from 0 = left to 10 = right. For this model to work the variable was further categorized to left, center and right. \
The objective is to see if we can classify the persons on their political scale according to socio-demographic predictor variable.

left center right NA’s

987 1149 125 97

0 1 2 3 4 5 6 7 8 9 10 NA’s

95 64 186 340 302 826 198 125 86 14 25 97

[1] “integer”

left center right NA’s

987 1149 125 97

tibble [1,089 × 7] (S3: tbl_df/tbl/data.frame)

$ age.na : num [1:1089] 26 54 41 47 48 60 44 51 26 79 …

$ interest.fac: Ord.factor w/ 4 levels “none at all”<..: 2 2 2 3 4 4 3 3 2 3 …

$ scale_cat : Factor w/ 3 levels “left”,“center”,..: 2 1 1 1 2 1 2 2 2 3 …

$ eduyrs.na : num [1:1089] 13 14 14 13 18 16 0 14 10 7 …

$ sat.dem.fac : Factor w/ 11 levels “0”,“1”,“2”,“3”,..: 8 6 8 6 10 9 6 6 5 5 …

$ yearpay : num [1:1089] 288000 72000 19200 26400 72000 …

$ vote.fac : Factor w/ 3 levels “Yes”,“No”,“Not eligible”: 2 1 1 1 1 1 2 1 1 1 …


### Have a quick look at the Data

<img src="ESS_DE_files/figure-html/unnamed-chunk-59-1.png" width="672" />

It is not possible to see a clear classifcation of groups by this plot.

<img src="ESS_DE_files/figure-html/unnamed-chunk-60-1.png" width="672" />

There can bee seen a small grouping on the left side of the plot (young people and middle education level).

### Prepare the Data for Training



### Create some easy Variables to access Data



### Train the Neural Network

Call:

svm(formula = scale_cat ~ ., data = train, kernel = “linear”, cost = 10,

scale = TRUE)

Parameters:

SVM-Type: C-classification

SVM-Kernel: linear

cost: 10

Number of Support Vectors: 833

( 385 408 40 )

Number of Classes: 3

Levels:

left center right


<img src="ESS_DE_files/figure-html/unnamed-chunk-64-1.png" width="672" />





The best cost parameter is 0.1.

<img src="ESS_DE_files/figure-html/unnamed-chunk-67-1.png" width="672" />

<img src="ESS_DE_files/figure-html/unnamed-chunk-68-1.png" width="672" />

The plots suggest, that linear may not be the right approach to get a classification right.

### Make Predictions



### Evaluate the Results

Confusion Matrix and Statistics

Reference

Prediction left center right

left 30 25 0

center 42 59 7

right 0 0 0

Overall Statistics

Accuracy : 0.546

95% CI : (0.4663, 0.624)

No Information Rate : 0.5153

P-Value [Acc > NIR] : 0.2405

Kappa : 0.109

Mcnemar’s Test P-Value : NA

Statistics by Class:

Class: left Class: center Class: right

Sensitivity 0.4167 0.7024 0.00000

Specificity 0.7253 0.3797 1.00000

Pos Pred Value 0.5455 0.5463 NaN

Neg Pred Value 0.6111 0.5455 0.95706

Prevalence 0.4417 0.5153 0.04294

Detection Rate 0.1840 0.3620 0.00000

Detection Prevalence 0.3374 0.6626 0.00000

Balanced Accuracy 0.5710 0.5411 0.50000


[**Interpretation**]{.underline}: the accuracy of the linear model is at a bit over 50%. It makes sense, as the descriptive plots hinted that there cannot be a straight "division" line.

### Try again with other parameters

Call:

svm(formula = scale_cat ~ ., data = train, kernel = “radial”, cost = 100000,

scale = TRUE)

Parameters:

SVM-Type: C-classification

SVM-Kernel: radial

cost: 100000

Number of Support Vectors: 661

( 300 322 39 )

Number of Classes: 3

Levels:

left center right


<img src="ESS_DE_files/figure-html/unnamed-chunk-72-1.png" width="672" />

Call:

best.tune(METHOD = svm, train.x = scale_cat ~ ., data = d.ess9_supportvec,

ranges = list(cost = c(0.001, 0.01, 0.1, 1, 5, 10, 100, 1000)),

kernel = “radial”, gamma = c(0.5, 1, 2, 3, 4))

Parameters:

SVM-Type: C-classification

SVM-Kernel: radial

cost: 1

Number of Support Vectors: 1016




<img src="ESS_DE_files/figure-html/unnamed-chunk-75-1.png" width="672" />

test_pred1

left center right

62 100 1

Confusion Matrix and Statistics

Reference

Prediction left center right

left 33 27 2

center 39 56 5

right 0 1 0

Overall Statistics

Accuracy : 0.546

95% CI : (0.4663, 0.624)

No Information Rate : 0.5153

P-Value [Acc > NIR] : 0.24051

Kappa : 0.1194

Mcnemar’s Test P-Value : 0.07689

Statistics by Class:

Class: left Class: center Class: right

Sensitivity 0.4583 0.6667 0.000000

Specificity 0.6813 0.4430 0.993590

Pos Pred Value 0.5323 0.5600 0.000000

Neg Pred Value 0.6139 0.5556 0.956790

Prevalence 0.4417 0.5153 0.042945

Detection Rate 0.2025 0.3436 0.000000

Detection Prevalence 0.3804 0.6135 0.006135

Balanced Accuracy 0.5698 0.5549 0.496795


[**Interpretation**]{.underline}: the accuracy of the linear model is at a bit over 50%. It has improved when compared to the linear classification approach but it is still unsatisfactory.

#### Tune costing





<img src="ESS_DE_files/figure-html/unnamed-chunk-79-1.png" width="672" />

With alsmost every additional cost the accuracy of the model increases. However, it stagnates with cost = 2. A small c indicates that the penalization for misclassification is small and therefore, it represents a soft margin. Inside the margins, the sample that is located there will not be penalized much.

[1] center center center center center left left left center left

[11] center left left left center center left center left center

[21] center center center center left center center left left center

[31] left center center left center center center left left left

[41] left center center left center left left center center center

[51] center center center left center left left center left center

[61] center left center center left center center left center left

[71] center center center left left center center center left center

[81] left center center center center left center center left center

[91] left center center center center center left center center left

[101] left center center left left left center center center center

[111] left center center left center center center center center center

[121] center left center left center center center center center left

[131] left left center left left left center left center center

[141] left center left left left center center center center center

[151] left center left left center center center left center center

[161] left left center left left center center left left left

[171] center center center center center left left left center center

[181] center center center center left center center center center center

[191] left center center left center center center left center center

[201] center center center left left center center left left center

[211] center center center left center center left center left center

[221] center center center center center center center center center center

[231] left left center center left center center center center center

[241] center left center center left center left center center left

[251] center center center center left left left center center center

[261] center center center center center left center center left left

[271] left center left center left center left left center center

[281] left center center left left left center center left center

[291] left left center left center center center center center center

[301] center center left left center center center center left center

[311] center center center center left left center center left center

[321] center center left left left center

Levels: left center right

Confusion Matrix and Statistics

test_pred_grid left center right

left 74 40 3

center 70 128 11

right 0 0 0

Overall Statistics

Accuracy : 0.6196

95% CI : (0.5645, 0.6726)

No Information Rate : 0.5153

P-Value [Acc > NIR] : 0.00009487

Kappa : 0.2558

Mcnemar’s Test P-Value : 0.00005979

Statistics by Class:

Class: left Class: center Class: right

Sensitivity 0.5139 0.7619 0.00000

Specificity 0.7637 0.4873 1.00000

Pos Pred Value 0.6325 0.6124 NaN

Neg Pred Value 0.6651 0.6581 0.95706

Prevalence 0.4417 0.5153 0.04294

Detection Rate 0.2270 0.3926 0.00000

Detection Prevalence 0.3589 0.6411 0.00000

Balanced Accuracy 0.6388 0.6246 0.50000

```

Interpretation: The classification of the political affiliation can surpass the 50% accuracy mark but much more is not achievable. This model is not made for the kernel = linear but rather kernel = radial. It is a much more complex data and it needs to be treated that way.

Conclusion

The question, whether the not-traditional political participation has differed during/after the pandemic (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9038938/) was the aim of this analysis with the “European Social Survey” 2018. As the linear regression shows, consumption of political/current affairs news increases with age and political interest. However, education has a small to none effect. The poisson model indicates, that for the same dependent variable the predictor variable age, political interest and gender have an influence on consumption. For the binomial model this analysis focused on whether persons posted something political or not. The results show that again age and political interest play a vital role. However, age is in a negative relationship to the dependent variable. The GAM-model is hinting that news consumption and age are non-linear. The last two models, NN and SVM, have some high limitations. The latter shows some low accuracy-level even with making it more complex and using the best cost number.